Uptake of anthropogenic CO2 is acidifying the oceans. Over the next 2000 years, this will modify the dissolution and preservation of sedimentary carbonate. By coupling new formulas for the positions of the calcite saturation horizon, zsat, the compensation depth, zcc, and the snowline, zsnow, to a biogeochemical model of the oceanic carbonate system, we evaluate how these horizons will change with ongoing ocean acidification. Our model is an extended Havardton-Bear-type box model, which includes novel kinetic descriptions for carbonate dissolution above, between, and below these critical depths. In the preindustrial ocean, zsat and zcc are at 3939 and 4750 m, respectively. When forced with the IS92a CO2 emission scenario, the model forecasts (1) that zsat will rise rapidly (“runaway” conditions) so that all deep water becomes undersaturated, (2) that zcc will also rise and over 1000 years will pass before it will be stabilized by the dissolution of previously deposited CaCO3, and (3) that zsnow will respond slowly to acidification, rising by ~1150 m during a 2000 year timeframe. A further simplified model that equates the compensation and saturation depths produces quantitatively different results. Finally, additional feedbacks due to acidification on calcification and increased atmospheric CO2 on organic matter productivity strongly affect the positions of the compensation horizons and their dynamics.